UC Santa Cruz

Power flow (PF) analysis is critical to power system operation and planning. Nowadays, renewable energy power generation has been widely installed in power grids because they are environmentally friendly. The high penetration of renewable energy brings significant fluctuations to the power system states. Probabilistic power flow (PPF) analysis aims to characterize the probability properties of voltage phasors with stochastic power injections.

Exploiting the impressive capability of neural networks (NNs) in complex function approximation, we utilize the NN as a rapid PF solver in real-time applications. Motivated by residual learning, the first work proposes a new NN structure based on the physical characteristics of PF equations. Specifically, we add a linear layer between the input and the output to the multilayer perceptron (MLP) structure. We design three schemes to initialize the NN weights for the shortcut connection layer based on the linearized PF equations. Numerical results show that the proposed approach outperforms existing NN frameworks in estimation accuracy and training convergence. However, the branch flow estimation accuracy of the NN-based methods on some benchmark systems is lower than the linearized PF-based method. The inherent reason is that the NN outputs are voltage angles instead of voltage angle differences, while the latter determines the branch flows. To further improve the branch flow estimates, the second work separates the training of voltage magnitudes and phase angles due to their different properties. We incorporate the errors of voltage angle differences into the training loss function.

Based on PF equations, optimal power flow (OPF) analysis minimizes the total generation cost while subject to other operational constraints. To help the independent system operator (ISO) clear the real-time energy market, we develop an unsupervised learning-based framework to solve the OPF problem rapidly. We employ a modified augmented Lagrangian function as the training loss. The multipliers are updated dynamically during the training process based on the degree of constraint violation. Numerical results show that the dynamic updates of the penalty weight coefficient improve the feasibility of solutions compared to the fixed pre-assigned coefficient.

To ensure the PF balance, the NN predicts a subset of decision variables, and the remaining variables are obtained by a subsequent PF solver. However, the variable splitting scheme introduces heavy computation complexity when it comes to computing gradients in backpropagation. Hence, in the fourth work, we aim to reduce the total computational time of the NN to enable a daily update of the NN. We propose a physics-informed gradient estimation method based on a semi-supervised learning framework. We employ ridge regression to obtain pseudo-optimal solutions and build a hybrid dataset. We propose a batch-mean gradient estimation method based on the linearized Jacobian model to speed up the training process. Numerical results show that the proposed gradient estimation method achieves a similar convergence rate as the ground truth Jacobian. Moreover, the proposed method rapidly obtains near-optimal solutions, which is appealing in real-time applications.